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Continuation for Thin Film Hydrodynamics and Related Scalar Problems. COMPUTATIONAL METHODS IN APPLIED SCIENCES 2019. [DOI: 10.1007/978-3-319-91494-7_13] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/12/2023]
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Di Pietro Martínez M, Hoyuelos M. Mean-field approach to diffusion with interaction: Darken equation and numerical validation. Phys Rev E 2018; 98:022121. [PMID: 30253616 DOI: 10.1103/physreve.98.022121] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2018] [Indexed: 06/08/2023]
Abstract
A mean-field theory for diffusion with interaction was introduced in Phys. Rev. E 92, 062118 (2015)PLEEE81539-375510.1103/PhysRevE.92.062118. Interaction effects are represented with a mean-field potential. Here we show that the potential can be directly related to the activity coefficient. In this context, we obtain an alternative derivation of the Darken equation, that relates collective diffusion coefficient and single particle diffusion coefficient (generally different in the presence of interactions). We also carry out a validation test of the model using, as a case study, effective interactions that reproduce Bose-Einstein statistics.
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Affiliation(s)
- M Di Pietro Martínez
- Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR - CONICET), Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Deán Funes 3350, 7600 Mar del Plata, Argentina
| | - M Hoyuelos
- Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR - CONICET), Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Deán Funes 3350, 7600 Mar del Plata, Argentina
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Beltrame P, Makhoul M, Joelson M. Deterministic particle transport in a ratchet flow. Phys Rev E 2016; 93:012208. [PMID: 26871074 DOI: 10.1103/physreve.93.012208] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2013] [Indexed: 11/07/2022]
Abstract
This study is motivated by the issue of the pumping of particle through a periodic modulated channel. We focus on a simplified deterministic model of small inertia particles within the Stokes flow framework that we call "ratchet flow." A path-following method is employed in the parameter space in order to retrace the scenario which from bounded periodic solutions leads to particle transport. Depending on whether the magnitude of the particle drag is moderate or large, two main transport mechanisms are identified in which the role of the parity symmetry of the flow differs. For large drag, transport is induced by flow asymmetry, while for moderate drag, since the full transport solution bifurcation structure already exists for symmetric settings, flow asymmetry only makes the transport effective. We analyzed the scenarios of current reversals for each mechanism as well as the role of synchronization. In particular we show that, for large drag, the particle drift is similar to phase slip in a synchronization problem.
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Affiliation(s)
- Philippe Beltrame
- Université d'Avignon et des Pays de Vaucluse-INRA, UMR1114 EMMAH, F-84914 Avignon, France
| | - Mounia Makhoul
- Université d'Avignon et des Pays de Vaucluse-INRA, UMR1114 EMMAH, F-84914 Avignon, France
| | - Maminirina Joelson
- Université d'Avignon et des Pays de Vaucluse-INRA, UMR1114 EMMAH, F-84914 Avignon, France
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Gernert R, Klapp SHL. Enhancement of mobility in an interacting colloidal system under feedback control. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022132. [PMID: 26382369 DOI: 10.1103/physreve.92.022132] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2015] [Indexed: 06/05/2023]
Abstract
Feedback control schemes are a promising way to manipulate transport properties of driven colloidal suspensions. In the present article, we suggest a feedback scheme to enhance the collective transport of colloidal particles with repulsive interactions through a one-dimensional tilted washboard potential. The control is modeled by a harmonic confining potential, mimicking an optical "trap," with the center of this trap moving with the (instantaneous) mean particle position. Our theoretical analysis is based on the Smoluchowski equation combined with dynamical density functional theory for systems with hard-core or ultrasoft (Gaussian) interactions. For either type of interaction, we find that the feedback control can lead to an enhancement of the mobility by several orders of magnitude relative to the uncontrolled case. The largest effects occur for intermediate stiffness of the trap and large particle numbers. Moreover, in some regions of the parameter space the feedback control induces oscillations of the mean velocity. Finally, we show that the enhancement of mobility is robust against a small time delay in implementing the feedback control.
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Affiliation(s)
- Robert Gernert
- Institut für Theoretische Physik, Sekr. EW 7-1, Technische Universität Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany
| | - Sabine H L Klapp
- Institut für Theoretische Physik, Sekr. EW 7-1, Technische Universität Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany
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Thiele U. Patterned deposition at moving contact lines. Adv Colloid Interface Sci 2014; 206:399-413. [PMID: 24331374 DOI: 10.1016/j.cis.2013.11.002] [Citation(s) in RCA: 66] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2013] [Revised: 11/07/2013] [Accepted: 11/07/2013] [Indexed: 01/09/2023]
Abstract
When a simple or complex liquid recedes from a smooth solid substrate it often leaves a homogeneous or structured deposit behind. In the case of a receding non-volatile pure liquid the deposit might be a liquid film or an arrangement of droplets depending on the receding speed of the meniscus and the wetting properties of the system. For complex liquids with volatile components as, e.g., polymer solutions and particle or surfactant suspensions, the deposit might be a homogeneous or structured layer of solute--with structures ranging from line patterns that can be orthogonal or parallel to the receding contact line via hexagonal or square arrangements of drops to complicated hierarchical structures. We review a number of recent experiments and modelling approaches with a particular focus on mesoscopic hydrodynamic long-wave models. The conclusion highlights open question and speculates about future developments.
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Affiliation(s)
- Uwe Thiele
- Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, UK; Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm Klemm Str. 9, D-48149 Münster, Germany.
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Pototsky A, Thiele U, Archer AJ. Coarsening modes of clusters of aggregating particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:032144. [PMID: 24730826 DOI: 10.1103/physreve.89.032144] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2014] [Indexed: 06/03/2023]
Abstract
There are two modes by which clusters of aggregating particles can coalesce: The clusters can merge either (i) by the Ostwald ripening process, in which particles diffuse from one cluster to the other while the cluster centers remain stationary, or (ii) by means of a cluster translation mode, in which the clusters move toward each other and join. To understand in detail the interplay between these different modes, we study a model system of hard particles with an additional attraction between them. The particles diffuse along narrow channels with smooth or periodically corrugated walls, so that the system may be treated as one-dimensional. When the attraction between the particles is strong enough, they aggregate to form clusters. The channel potential influences whether clusters can move easily or not through the system and can prevent cluster motion. We use dynamical density functional theory to study the dynamics of the aggregation process, focusing in particular on the coalescence of two equal-sized clusters. As long as the particle hard-core diameter is nonzero, we find that the coalescence process can be halted by a sufficiently strong corrugation potential. The period of the potential determines the size of the final stable clusters. For the case of smooth channel walls, we demonstrate that there is a crossover in the dominance of the two different coarsening modes, which depends on the strength of the attraction between particles, the cluster sizes, and the separation distance between clusters.
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Affiliation(s)
- Andrey Pototsky
- Department of Mathematics, Faculty of Science, Engineering and Technology, Swinburne University of Technology, Hawthorn, Victoria, 3122, Australia
| | - Uwe Thiele
- Department of Mathematical Science, Loughborough University, Loughborough LE11 3TU, United Kingdom and Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm Klemm Strasse 9, D-48149 Münster, Germany
| | - Andrew J Archer
- Department of Mathematical Science, Loughborough University, Loughborough LE11 3TU, United Kingdom
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Lichtner K, Klapp SHL. Spinodal decomposition of a binary magnetic fluid confined to a surface. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:032301. [PMID: 24125262 DOI: 10.1103/physreve.88.032301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2013] [Revised: 08/16/2013] [Indexed: 06/02/2023]
Abstract
In our previous work [J. Chem. Phys. 136, 024502 (2012)], we reported a demixing phase transition of a quasi-two-dimensional, binary Heisenberg fluid mixture driven by the ferromagnetic interactions of the magnetic species. Here, we present a theoretical study for the time-dependent coarsening occurring within the two-phase region in the density-concentration plane, also known as spinodal decomposition. Our investigations are based on dynamical density functional theory (DDFT). The particles in the mixture are modeled as Gaussian soft spheres on a two-dimensional surface, where one component carries a classical spin of Heisenberg type. To investigate the two-phase region, we first present a linear stability analysis with respect to small, harmonic density perturbations. Second, to capture nonlinear effects, we calculate time-dependent structure factors by combining DDFT with Percus' test particle method. For the growth of the average domain size l during spinodal decomposition with time t, we observe a power-law behavior l∝t^{δ_{α}} with δ_{m}≃0.333 for the magnetic species and δ_{n}≃0.323 for the nonmagnetic species.
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Affiliation(s)
- K Lichtner
- Institute of Theoretical Physics, Secr. EW 7-1, Technical University Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
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Jäger S, Klapp SHL. Rotational ratchets with dipolar interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:061402. [PMID: 23367945 DOI: 10.1103/physreve.86.061402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2012] [Indexed: 06/01/2023]
Abstract
We report results from a computer simulation study on the rotational ratchet effect in systems of magnetic particles interacting via dipolar interactions. The ratchet effect consists of directed rotations of the particles in an oscillating magnetic field, which lacks a net rotating component. Our investigations are based on Brownian dynamics simulations of such many-particle systems. We investigate the influence of both the random and deterministic contributions to the equations of motion on the ratchet effect. As a main result, we show that dipolar interactions can have an enhancing as well as a dampening effect on the ratchet behavior depending on the dipolar coupling strength of the system under consideration. The enhancement is shown to be caused by an increase in the effective field on a particle generated by neighboring magnetic particles, while the dampening is due to restricted rotational motion in the effective field. Moreover, we find a nontrivial influence of the short-range, repulsive interaction between the particles.
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Affiliation(s)
- Sebastian Jäger
- Institute of Theoretical Physics, Technical University Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany.
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Lichtner K, Pototsky A, Klapp SHL. Feedback-induced oscillations in one-dimensional colloidal transport. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:051405. [PMID: 23214782 DOI: 10.1103/physreve.86.051405] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2012] [Indexed: 06/01/2023]
Abstract
We investigate a driven, one-dimensional system of colloidal particles in a periodically corrugated narrow channel subject to a time-delayed feedback control. Our goal is to identify conditions under which the control induces oscillatory, time-periodic states. The investigations are based on the Fokker-Planck equation involving the density distribution of the system. First, by using the numerical continuation technique, we determine the linear stability of a stationary density. Second, the nonlinear regimes are analyzed by studying numerically the temporal evolution of the first moment of the density distribution. In this way we construct a bifurcation diagram revealing the nature of the instability. Apart from the case of a system with periodic boundary conditions, we also consider a microchannel of finite length. Finally, we study the influence of (repulsive) particle interactions based on dynamical density functional theory.
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Affiliation(s)
- K Lichtner
- Institute of Theoretical Physics, Secr EW 7-1, Technical University Berlin, Hardenbergstr 36, D-10623 Berlin, Germany.
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Lichtner K, Archer AJ, Klapp SHL. Phase separation dynamics in a two-dimensional magnetic mixture. J Chem Phys 2012; 136:024502. [DOI: 10.1063/1.3674270] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Reinhardt J, Brader JM. Dynamics of localized particles from density functional theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:011404. [PMID: 22400570 DOI: 10.1103/physreve.85.011404] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2011] [Revised: 11/23/2011] [Indexed: 05/31/2023]
Abstract
A fundamental assumption of the dynamical density functional theory (DDFT) of colloidal systems is that a grand-canonical free-energy functional may be employed to generate the thermodynamic driving forces. Using one-dimensional hard rods as a model system, we analyze the validity of this key assumption and show that unphysical self-interactions of the tagged particle density fields, arising from coupling to a particle reservoir, are responsible for the excessively fast relaxation predicted by the theory. Moreover, our findings suggest that even employing a canonical functional would not lead to an improvement for many-particle systems, if only the total density is considered. We present several possible schemes to suppress these effects by incorporating tagged densities. When applied to confined systems, we demonstrate, using a simple example, that DDFT necessarily leads to delocalized tagged particle density distributions, which do not respect the fundamental geometrical constraints apparent in Brownian dynamics simulation data. The implication of these results for possible applications of DDFT to treat the glass transition are discussed.
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Affiliation(s)
- J Reinhardt
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
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